The electric field intensity due to an infinite sheet of charge can be calculated using Gauss's Law.

Gauss's Law states that the electric flux through any closed surface is equal to the total charge enclosed by that surface divided by the permittivity of free space (ε0).

For an infinite sheet of charge, the electric field is constant and perpendicular to the sheet. We can consider a Gaussian surface in the form of a cylinder with one of its circular faces inside the sheet and the other outside. The electric flux through this cylinder is given by:

Φ = E * A = (E)(2πrh)

where E is the electric field intensity, A is the area of the circular face of the cylinder, r is the radius of the circular face, and h is the height of the cylinder.

Since the electric field is constant and perpendicular to the sheet, the electric flux through the cylinder is given by:

Φ = (σ / ε0) * A

where σ is the charge density of the sheet.

Equating the two expressions for electric flux, we have:

(E)(2πrh) = (σ / ε0) * A

Simplifying, we find:

E = (σ / 2ε0)

Therefore, the electric field intensity due to an infinite sheet of charge is given by:

E = σ / (2ε0)

where σ is the charge density of the sheet and ε0 is the permittivity of free space.